Explicit Markov counting model of inter-spike interval time series

In this paper the inter-spike intervals (ISI) time series are recorded in awake, behaving macaque monkeys and their differences are modeled as a counting explicit finite Markov chain. The average length of time series was 3050 samples. The parameters investigated were: the state probability, the transition probability and normalized count histogram of the Markov chain, as well as ISI interval and ISI difference associated to each state of Markov model separately. As a control parameter, for each series pseudorandom Gaussian and uniform series with same mean and standard deviation, as well as isodistributional surrogates were generated. An unexpected conclusion is that the state and the transition probabilities, as well as the count histogram, correspond to the exact formulae that are derived for the differentials of independent and identically distributed (i.i.d.) random data series.